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4 year oldIn a statement, the 87-year-old judge said the treatment was having "positive results" and she was "fully able" to continue in her post.
Ms Ginsburg said a scan had revealed lesions on her liver, but the chemotherapy had helped to reduce them.
As the court's most senior liberal justice, her health is closely watched.
She has received hospital treatment a number of times in recent years but has returned swiftly to work on each occasion.
"On May 19, I began a course of chemotherapy to treat a recurrence of cancer," Ms Ginsburg said in her statement.
"The chemotherapy course... is yielding positive results," she added. "My most recent scan on 7 July indicated [a] significant reduction of the liver lesions and no new disease.
"I am tolerating chemotherapy well and am encouraged by the success of my current treatment," she said. "I will continue bi-weekly chemotherapy to keep my cancer at bay."
Supreme Court justices serve for life or until they choose to retire, and supporters have expressed concern that if anything were to happen to Ms Ginsburg a more conservative judge might replace her while President Donald Trump, a Republican, remains in office.
"I have often said I would remain a member of the Court as long as I can do the job full steam," Ms Ginsburg said in the statement. "I remain fully able to do that."
Mr Trump has appointed two judges since taking office, leaving the current bench with a 5-4 conservative leaning.
In May, Ms Ginsburg underwent non-surgical treatment for a benign gallbladder condition, and participated in the Supreme Court's oral arguments from hospital. She has been treated for cancer four times in 20 years, including two separate bouts last year.
Earlier this week, she was released from Baltimore's Johns Hopkins Hospital after a day of treatment for a possible infection. Ms Ginsburg is now "home and doing well", the court said on Tuesday.
Despite her several health setbacks, Ms Ginsburg had not missed a single day of oral arguments in her 25 years on the court until last January, when she worked from home while recovering from surgery.
Joan Ruth Bader was born in Brooklyn, New York, in 1933 to Jewish immigrant parents. At 17 years old, she lost her mother to cancer.
She attended Cornell University, where she met her husband, Marty Ginsburg. The pair had two children and remained together for 56 years, until Marty's death in 2010.
Both attended Harvard Law School. When Justice Ginsburg attended in 1956, one year behind her husband, she was one of nine women to enrol. While there, she and her female cohort were famously asked by the dean to justify taking the spot of a man in his school.
Ms Ginsburg later transferred to Columbia Law School in New York, becoming the first woman to work at both school's law reviews.
Despite her academic success, she struggled to find work.
"Not a law firm in the entire city of New York would employ me," she once said. "I struck out on three grounds: I was Jewish, a woman and a mother."
She went on to become a professor at Rutgers Law School in 1963, and co-founded the Women's Rights Project at the American Civil Liberties Union (ACLU). As the ACLU's general counsel, Ms Ginsburg took up a series of gender discrimination cases, six of which saw her arguing before the Supreme Court.
In part due to her husband's enthusiastic lobbying, Ms Ginsburg was nominated to the Supreme Court in 1993 by then President Bill Clinton. She became the second woman in US history nominated to the august body.
During her years on the court, as the bench has become more conservative, she has increasingly moved to the left, gaining a reputation for her spirited dissents.
And in recent years, she has grown into a pop culture phenomenon.
In part due to her scathing dissents, Ms Ginsburg became the subject of a Tumblr account called Notorious RBG - a nod to the late rapper, The Notorious BIG. She has been played by actress and comedian Kate McKinnon on Saturday Night Live, and has her likeness painted on T-shirts, mugs and posters.
"I'm 84 years old," Ms Ginsburg says about her newfound fame in the 2018 documentary RBG.
"And everyone wants to take their picture with me."
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